The instance_activate_region() and such functions are pretty easy to use, just supply the view top x coord, view width, etc as arguments. All in one room is much more convenient when level designing, too, so I'm really not sure why you'd want to split it all into smaller rooms.
Unfortunately, those functions don't work the same way the frozen zone does. And, perhaps more importantly, they're slow. (Of course, everything in GM is slow, but this in particular will get really bad if you have a lot of objects. Perhaps, for this particular game, in which there would probably be only a few objects per screen, it would be fine, but in general I wouldn't recommend it.)
Using multiple rooms is an inefficient system
Not really. It's a bit more difficult for the game's creator, but it's far more efficient in terms of resources. Although the room-to-room transitions will be slower than simply moving the view, you'll save a lot on both memory and CPU usage.
Linking images is annoying and difficult
I'm assuming you mean making the room edges match up? You'll have that problem regardless of the system you use, I'm afraid. Using the view method will make it slightly more convenient if you're using tiles, but only slightly.
programming objects to affect objects outside the same room (e.g. a button on screen 30x47 that opens a door on screen 30x49) is far more touchy.
This is true. Certainly, if you want an enemy or something to continue running around even when you're not in its "room," then the view method would be preferable. But since you mentioned deactivating instances outside the view, it really does make more sense to use the room system.
It should be pointed out that the whole efficiency thing might be moot, making the view method just fine, depending on how simple the game is. Certainly, if you're simply using a few tilesets like in Knytt to design the screens, and gradients for the backgrounds, that's fine.
But a game with similar room changing - An Untitled Story - could never hope to do this. Every screen has a PNG background and foreground image, both 640x480. The PNG compression keeps them small enough on your hard drive, but they obviously need to be uncompressed to be displayed. If it used your view system,
most home computers wouldn't be able to run it because of the massive memory usage.